A finite set of local moves for Kirby calculus
Bruno Martelli
TL;DR
This paper introduces a finite set of local moves, including handle-slides and blow-downs/ups, that can transform any two surgery presentations of the same 3-manifold into each other.
Contribution
It provides a finite set of local moves for Kirby calculus, simplifying the process of relating different surgery presentations of 3-manifolds.
Findings
Finite set of moves connects any two surgery presentations
Moves include handle-slides and specific blow-downs/ups
Simplifies Kirby calculus for 3-manifolds
Abstract
We exhibit a finite set of local moves that connect any two surgery presentations of the same 3-manifold via framed links in the three-sphere. The moves are handle-slides and blow-downs/ups of a particular simple kind.
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